Under a new law, police and officers with the state's Society for the Prevention of Cruelty to Animals could fine a driver $250 - $1,000 for giving a four-legged family member free rein of the car while it's moving.

"You should not be driving down the road under any circumstances with a dog driving the car," Elyse Coffey, a spokeswoman for the New Jersey Motor Vehicle Commission, told Fox News Radio on Monday. "We don't want dogs driving with the steering wheel, and we don't want cats who sit on the dashboard."

Some in the Garden State scoffed at the news, but New Jersey is not the only state to consider or take up legislation to curb what transportation experts consider another contributor to distracted driving.

Arizona, Connecticut and Maine residents can be penalized under distracted-driving laws if they're driving with a pet in their lap. In Hawaii, drivers are not allowed to drive with pets in their laps; Rhode Island and Oregon are considering doing the same.

According to a 2011 pet passenger safety survey by AAA and Kurgo pet products, 65 percent of dog owners admitted to engaging in at least one potentially distracting activity while driving with their dog.

In that group, 52 percent said that activity included petting their pet, even when the animal was in the backseat. According to the AAA Foundation for Traffic Safety, looking away from the road for just two seconds can double a driver's risk of being in a crash.

"The devastation to your pet and any other passengers can be incredible" in the event of an accident, Heather Hunter, a AAA spokeswoman, told ABC News today.

In Cranberry, Pa., David Reed ran a red light in April and crashed into another vehicle after his dog crawled into his lap. His 2-year-old basset hound hit the windshield and landed on the dashboard but didn't sustain any injuries.

He and his daughter were not hurt but the other driver had to be treated for injuries.

"You see people doing it [driving with a dog] all the time," he said. "You just don't think it's going to happen. … I never gave it a thought - my pet being a distraction to me when I was driving or anything."

AAA's Hunter said restraining a pet while traveling in a vehicle minimized distractions to the driver, protected other passengers and also allowed emergency personnel to get to the vehicle and treat passengers if an accident occurred. Restraints also stop a pet from running off when a door is opened.

"You've wouldn't drive with your child in your lap, we want to keep them safe, just as you would your child," Dr. Kat Miller of the ASPCA told ABC News.

"The length of the tether allows him to sit up comfortably and sit up normally but not roam around the back seat," added Dr. Miller.

Gordie Spater, Kurgo's president, said that many pet owners simply didn't know that car restraints existed for their pets and that they were easy to use and relatively inexpensive.

He said that even though his company did not advocate laws such as New Jersey's, it had partnered with AAA and Toyota to get the message out.

"Our biggest thing is to get the word out that [restraints] are available," he said. "Things are available [and] the cost is low. You should be doing this."

Click here for a 25 percent discount off harnesses at the ASPCA's online store using the code SAFETY. The deal is available through Friday.

And click here for tips on traveling safely with your pet this summer and any time of the year.